0000000000548147

AUTHOR

Miguel García-bravo

showing 2 related works from this author

Bi-Lipschitz invariance of planar BV- and W1,1-extension domains

2021

We prove that a bi-Lipschitz image of a planar $BV$-extension domain is also a $BV$-extension domain, and that a bi-Lipschitz image of a planar $W^{1,1}$-extension domain is again a $W^{1,1}$-extension domain.

Mathematics - Functional AnalysisMathematics - Classical Analysis and ODEsBV-extensionClassical Analysis and ODEs (math.CA)FOS: MathematicsSobolev extension46E35funktionaalianalyysiFunctional Analysis (math.FA)
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Strong BV-extension and W1,1-extension domains

2021

We show that a bounded domain in a Euclidean space is a $W^{1,1}$-extension domain if and only if it is a strong $BV$-extension domain. In the planar case, bounded and strong $BV$-extension domains are shown to be exactly those $BV$-extension domains for which the set $\partial\Omega \setminus \bigcup_{i} \overline{\Omega}_i$ is purely $1$-unrectifiable, where $\Omega_i$ are the open connected components of $\mathbb{R}^2\setminus\overline{\Omega}$.

46E35 26B30Mathematics - Metric GeometrymatematiikkaMathematics::Complex VariablesBV-extensionFOS: MathematicsSobolev extensionMetric Geometry (math.MG)Analysis
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